Answer A: Anthropic Claude Opus 4.6
1. Original Market Equilibrium Price and Quantity Set Qd = Qs: 1000 - 20P = 100 + 30P 900 = 50P P* = 18 dollars per liter Q* = 1000 - 20(18) = 1000 - 360 = 640 thousand liters per day (Check: Qs = 100 + 30(18) = 100 + 540 = 640. Confirmed.) The original equilibrium price is $18 per liter and the equilibrium quantity is 640 thousand liters per day. 2. New Equilibrium Quantity After the Tax A specific tax of $5 per liter is imposed on sellers. This means sellers receive the consumer price minus the tax. If Pc is the price consumers pay, then the price sellers receive is Ps = Pc - 5. The new supply condition (...
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1. Original Market Equilibrium Price and Quantity Set Qd = Qs: 1000 - 20P = 100 + 30P 900 = 50P P* = 18 dollars per liter Q* = 1000 - 20(18) = 1000 - 360 = 640 thousand liters per day (Check: Qs = 100 + 30(18) = 100 + 540 = 640. Confirmed.) The original equilibrium price is $18 per liter and the equilibrium quantity is 640 thousand liters per day. 2. New Equilibrium Quantity After the Tax A specific tax of $5 per liter is imposed on sellers. This means sellers receive the consumer price minus the tax. If Pc is the price consumers pay, then the price sellers receive is Ps = Pc - 5. The new supply condition (in terms of the consumer price) becomes: Qs = 100 + 30(Pc - 5) = 100 + 30Pc - 150 = -50 + 30Pc Set the new supply equal to demand: 1000 - 20Pc = -50 + 30Pc 1050 = 50Pc Pc = 21 dollars per liter New equilibrium quantity: Q_tax = 1000 - 20(21) = 1000 - 420 = 580 thousand liters per day (Check: Qs = -50 + 30(21) = -50 + 630 = 580. Confirmed.) The new equilibrium quantity is 580 thousand liters per day. 3. Price Paid by Consumers and Price Received by Sellers Price paid by consumers: Pc = $21 per liter Price received by sellers: Ps = 21 - 5 = $16 per liter Consumers pay $3 more than the original price, and sellers receive $2 less than the original price. The $5 tax is shared: $3 borne by consumers and $2 borne by sellers. 4. Total Tax Revenue Per Day Tax revenue = tax per unit times quantity sold Tax revenue = 5 times 580 = 2900 thousand dollars per day (i.e., $2,900,000 per day) 5. Change in Consumer Surplus Consumer surplus is the triangle between the demand curve and the price line. Before the tax: The demand curve intercept (where Qd = 0) is P = 50 (from 1000 - 20P = 0). CS_before = 0.5 times (50 - 18) times 640 = 0.5 times 32 times 640 = 10,240 thousand dollars per day After the tax (consumers pay Pc = 21): CS_after = 0.5 times (50 - 21) times 580 = 0.5 times 29 times 580 = 8,410 thousand dollars per day Change in consumer surplus = 8,410 - 10,240 = -1,830 thousand dollars per day Consumer surplus falls by 1,830 thousand dollars per day ($1,830,000 per day). 6. Change in Producer Surplus The supply curve intercept (where Qs = 0) is P = -100/30 = -10/3 (approximately -3.33). Since this is negative, the supply curve hits Q = 0 at a negative price, meaning at P = 0 the quantity supplied is positive (Qs = 100). For the geometry, we use the supply curve intercept price of -10/3. Before the tax: PS_before = 0.5 times (18 - (-10/3)) times 640 = 0.5 times (18 + 10/3) times 640 = 0.5 times (64/3) times 640 = 0.5 times 640 times 64/3 = 320 times 64/3 = 20,480/3 = 6,826.67 thousand dollars per day After the tax (sellers receive Ps = 16): PS_after = 0.5 times (16 - (-10/3)) times 580 = 0.5 times (16 + 10/3) times 580 = 0.5 times (58/3) times 580 = 0.5 times 580 times 58/3 = 290 times 58/3 = 16,820/3 = 5,606.67 thousand dollars per day Change in producer surplus = 5,606.67 - 6,826.67 = -1,220 thousand dollars per day Producer surplus falls by 1,220 thousand dollars per day ($1,220,000 per day). 7. Deadweight Loss Deadweight loss is the net loss to society: the total loss in consumer and producer surplus minus the tax revenue collected by the government. Total surplus loss = 1,830 + 1,220 = 3,050 thousand dollars per day Tax revenue = 2,900 thousand dollars per day Deadweight loss = 3,050 - 2,900 = 150 thousand dollars per day ($150,000 per day) Alternatively, using the triangle formula: DWL = 0.5 times tax times (change in quantity) = 0.5 times 5 times (640 - 580) = 0.5 times 5 times 60 = 150 thousand dollars per day. Confirmed. 8. Why Deadweight Loss Arises Deadweight loss arises because the tax drives a wedge between the price consumers pay and the price sellers receive, causing the market quantity to fall below the efficient level. Before the tax, all units between 580 and 640 thousand liters were traded because buyers valued them more than it cost sellers to produce them. After the tax, these mutually beneficial transactions no longer occur: the tax makes the effective cost to buyers higher than their willingness to pay, even though the actual production cost is still below what buyers would have been willing to pay in the absence of the tax. The surplus that would have been generated by these lost transactions is not captured by anyone — not by consumers, not by producers, and not by the government as tax revenue. This irrecoverable loss of surplus is the deadweight loss, and it represents the efficiency cost of the tax distorting market behavior away from the competitive equilibrium.
Result
Winning Votes
3 / 3
Average Score
Total Score
Overall Comments
Answer A is thorough, numerically precise, and methodologically sound throughout. It correctly solves all eight parts, shows clear step-by-step calculations, verifies results with checks, and uses proper geometric formulas. The explanation of deadweight loss is particularly strong, connecting the tax wedge to lost mutually beneficial trades in a nuanced way. The handling of the supply curve intercept (negative price) is explicitly addressed, demonstrating conceptual depth. Minor stylistic choices (using 'times' instead of multiplication symbols) do not detract from quality.
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Correctness
Weight 45%All numerical results are correct: P*=18, Q*=640, Pc=21, Ps=16, Qt=580, Tax Revenue=2900, ΔCS=-1830, ΔPS=-1220, DWL=150. The supply intercept is correctly identified as -10/3 and used properly in surplus calculations. Verification checks confirm consistency.
Reasoning Quality
Weight 20%Answer A explicitly derives the tax wedge mechanism, verifies equilibrium on both sides, addresses the negative supply intercept, and confirms DWL using two independent methods (surplus difference and triangle formula). The reasoning chain is tight and transparent.
Completeness
Weight 15%All eight parts are fully addressed with detailed calculations, intermediate steps, unit labels, and a cross-verification of DWL. The answer leaves no required element unaddressed.
Clarity
Weight 10%Answer A is clearly structured with numbered sections, logical flow, and explicit labeling of variables. The use of 'times' instead of the multiplication symbol is a minor stylistic quirk but does not impede readability.
Instruction Following
Weight 10%Answer A follows all instructions: shows key calculation steps, uses standard geometry formulas for surplus areas, addresses all eight parts, and uses the correct units (thousands of liters per day, dollars per liter).
Total Score
Overall Comments
Answer A provides a comprehensive and perfectly accurate solution to all parts of the problem. Its calculations are meticulously detailed, especially in the breakdown of consumer and producer surplus before and after the tax, which directly applies the requested geometry formulas for surplus areas. The explanation of deadweight loss is clear, insightful, and well-articulated, demonstrating a strong understanding of the economic concepts.
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Correctness
Weight 45%All calculations and final numerical results are perfectly correct for every part of the problem.
Reasoning Quality
Weight 20%The reasoning is exceptionally sound, with clear logical progression for all steps. The detailed breakdown of surplus calculations (before and after) demonstrates a deep understanding.
Completeness
Weight 15%All eight parts of the prompt are fully addressed, with all required calculations and explanations provided.
Clarity
Weight 10%The answer is very clear, well-organized, and easy to follow. Calculation steps are presented logically, and the explanation of deadweight loss is articulate.
Instruction Following
Weight 10%The answer meticulously follows all instructions, including showing key calculation steps clearly and using standard geometry formulas for surplus areas by calculating the before and after triangle areas.
Total Score
Overall Comments
Answer A is fully correct, numerically consistent, and notably strong because it computes all requested quantities and also shows both before-and-after surplus levels using standard triangle geometry. It clearly distinguishes consumer and seller prices after the tax, handles units properly, and gives two consistent ways to verify deadweight loss. Its main weakness is that it is somewhat longer than necessary and includes a few wording choices that could be tighter, but the economics and calculations are sound.
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Correctness
Weight 45%All core results are correct: pre-tax equilibrium 18 and 640, post-tax quantity 580, consumer price 21, seller price 16, tax revenue 2900 thousand dollars, change in consumer surplus -1830, change in producer surplus -1220, and deadweight loss 150. The surplus geometry is handled correctly, including the negative supply intercept.
Reasoning Quality
Weight 20%The reasoning is systematic and transparent. It correctly introduces the tax wedge, rewrites supply in terms of consumer price, and checks results for consistency. It also confirms deadweight loss using two methods, which strengthens the logic.
Completeness
Weight 15%It answers all eight parts fully and includes key intermediate steps, intercepts, before-and-after surplus values, incidence interpretation, unit interpretation, and a full verbal explanation of deadweight loss.
Clarity
Weight 10%The organization is clear, with each part labeled and calculations shown. The answer is slightly verbose, but still readable and instructional.
Instruction Following
Weight 10%It follows the prompt closely by showing key calculation steps and using standard geometry formulas for surplus areas. It also preserves the requested educational style and implied units.